Path to Abstraction

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Path to Abstraction

By Victoria Gaber


Throughout the elementary years, children are following their own internal path towards abstracting concepts of math, language, the sciences, and the rest. The weeks right after the holidays can tend be a time of serious academic growth as the students remember the feeling of focusing on work after a long break from their regular 3-hour work cycle. Students can sometimes become very eager to “abstract” a concept, or to move solely to paper rather than continuing with materials. Though it can be challenging, it is imperative that students continue to work with the materials even throughout the exciting process when abstraction is near. When a student, for example, is beginning to understand the written work of multiplying a 4- or 5-digit number by a 2-digit multiplier, the material is vital for “proving” the work and reinforcing the concept. As adults, it can be easy to see those glorious moments when things start to “click” for the kids, and we can even sometimes be a hinderance by cheering them on and excitedly rushing them to more paper and another problem.

This is especially important in all the math areas- where we most commonly feel rushed to abstraction- as students will have tiny missteps throughout large operations over the course of reaching mastery. Forgetting to carry over just one time in a large problem can have consequences that are tedious to repair over and over again. Supported by the material, children can return exactly to the point in the problem that challenged their math fact mastery, make the correction, and then feel supported enough to continue the work. This support allows the children to experience failure and come back from it.  This support also plays a substantial role in fostering independence, which is a highly necessary characteristic for the Montessori classroom and for students who will one day (too soon) be functioning adults leading lives of their own.  The best way we can support the process of abstraction as Montessorians is to take away the teacher or adult as the means of correction and continue relying on the material to be that control of error.

Well, what is the role of the adult in the presence of children’s learning? From the Montessori teacher perspective, our biggest role is as the observer. In order to know what to present to children next, we watch and listen. Wherever the child meets struggle, we offer support the next day or the next week in a different way. The “in a different way” part is particularly important. In this day and age, we are all familiar with the reality that learning styles vary from child to child. Research suggests that people actually have a variety of learning styles that can change over time and even throughout the day. Many children even operate with a multitude of learning modalities at once and will grasp new information if it is presented in multiple ways. The genius of Montessori materials is not just in the concrete didactic physical representation of the learning tools, but is also in the variety of learning modalities represented in the lesson.

Here’s an example of a varied lesson. This month, upper elementary students are finishing up a study of sound. Inside, we talked about the Doppler Effect. While talking, we drew artistic representations of this effect (having already learned about sound as waves). Then, we processed how that might be experienced in life. We watched a video of this happening with a car horn honking as it passed a group of children. Then, we experienced it for ourselves by blowing a whistle as a student rides by quickly on a bicycle. Within this lesson we covered as many learning styles as we could imagine! Children got to process both with verbal and auditory skills. There was the option to creatively figure it out with art. We had an audiovisual representation with a video. A very physical representation took place outside in the driveway. This varied teaching style occurs in lesson presentations across the curriculum.  It is a beautiful benefit for the children is that if something isn’t quite “sticking”, there’s always something else to try.  As these students continue their paths to abstraction for the rest of their childhoods, their classroom will be a safe place for falling down and getting up again.